You want to choose n classes for your next semester, for which you know the amount of hours (between 1 and 10) you will need to spend on the class every week and the number of credits (between 1 and 3) you will earn after taking it all integers). You also calculated the "learning" number for each class, that represents how much you will learn in the course based on previous courses you have taken. Considering you want to work for at most 40 hours a week, and want to maximize the number of credits you can take in the semester, among all the course selections that maximize credit and have no more than 40 hours of work per week, you would like to choose one that maximizes "learning" for you. Solve for O(n) time using Dynamic programming with following steps: 1) Describe algorithm 2) Proof of correctness for algorithm 3) Running time of algorithm